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PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph

  • Christopher EngströmEmail author
  • Sergei Silvestrov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 179)

Abstract

In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.

Keywords

PageRank Graph Random walk Block matrix 

Notes

Acknowledgements

This research was supported in part by the Swedish Research Council (621- 2007-6338), Swedish Foundation for International Cooperation in Research and Higher Education (STINT), Royal Swedish Academy of Sciences, Royal Physiographic Society in Lund and Crafoord Foundation.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Division of Applied Mathematics, School of EducationCulture and Communication, Mälardalen UniversityVästeråsSweden

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